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Ultrasonic Characterization of Intermetallics Raja Ram Yadav and Devraj Singh Department of Physics, University of Allahabad, India e-mail . physics @ nde.vsnl.net.in Contact

Abstract

Ultrasonic absorption in GdP and GdAs has been calculated at low temperatures from 2K to 80K. Ultrasonic attenuation due to electron-phonon interaction affected with electrical resistivity and elastic parameters is very small as compared to pure metals and temperature dependence of absorption is of the same nature as in pure metals except some anomalous kinks.

Theory

Ultrasonic offers the possibility to detect and characterize microstructural properties as well as flaws in materials, controlling material behaviour based on the physical mechanisms to predict future performance of the materials. Structural inhomogeneties, elastic parameters, nonlinearity parameters are well connected with the frequency or temperature dependence of ultrasonic attenuation mechanisms.

In the low temperature region and in metals the most important factor contributing to ultrasonic attenuation is the electron-phonon interaction [1,2,3].

Although a number of studies have been made in metals at low temperature region, only few results are available in intermetallics. The Rare - earth monopnictides RX (X = N, P As, Sb, Bi) are quiet interesting as the observed anomalous physical properties of these semimetallics have attracted much attention in recent year [4-8]. In order to study the behaviour of ultrasonic attenuation, we have taken GdP, GdAs single crystals. When ultrasonic wave is passed through a solid, the coupling between conduction electron and acoustical phonon occurs below 80K. In this investigation electron-lattice interaction characterizing the compounds GdP, GdAs have been studied with the help of electrical resistivity and elastic parameters.

The attenuation due to shear and compressional viscosity of the lattice at the low temperatures are [9]

	(1)
	(2)
	(3)

Where

he	stands for electron - viscosity
VL	velocity of longitudinal wave
VS	Velocity of Shear wave
f	frequency of the wave
c	compressional viscosity
r	density of the material
R	electrical resistivity
N	electronic density
h	Planck's constant divided by 2p

We have computed the temperature dependence of second order elastic constants SOEC (C₁₁, C₁₂, C₄₄) for the evaluations of velocity of the ultrasonic wave with method described by Mori and Hiki [10].

Results and Conclusions

The result of values of R (electrical resistivity) [11] and calculated h_e (election - viscosity), (a/f²)_Long and (a/f²)_Shear are presented in Tables 1, 2. for GdP and GdAs respectively.

T (K)	R(10-8W m)	he(10-4 Kg/ms)	(a/f2)L(10-15 Nps2/m)	(a/f2)S( 10-15 Nps2/m)
2	8.6670	1.54292	0.0285151	0.149700
5	10.3330	1.29416	0.0239177	0.125564
10	14.1667	0.943942	0.0174452	0.091585
20	22.0000	0.607819	0.0112331	0.0589712
30	23.3333	0.573039	0.0105895	0.0555908
40	24.6667	0.541976	0.0100107	0.0525661
50	26.000	0.514004	0.00948045	0.0498293
60	27.3333	0.488842	0.00897615	0.0473694
70	32.5000	0.411035	0.00754624	0.0398093
80	35.0000	0.381664	0.00698552	0.0369489
Table 1: Electrical resistivity (R), Viscosity (he), (a/f2)L for longitudinal wave and (a/f2)S for shear wave of GdP at temperature (T) region from 2K to 80K.

T (K)	R(10-8Wm)	he(10-4 Kg/ms)	(a/f2)L(10-15 Nps2/m)	(a/f2)S( 10-15 Nps2/m)
2	4.75	2.66798	0.0579935	0.329803
5	6.33	2.00204	0.0435181	0.247483
10	8.33	1.52135	0.0330694	0.188062
20	13.50	0.938722	0.0204051	0.116037
30	15.30	0.817547	0.0177626	0.101041
40	17.50	0.724058	0.015707	0.08946
50	18.75	0.675727	0.0146207	0.083454
60	21.50	0.589236	0.0127066	0.0727365
70	25.00	0.506684	0.010838	0.065121
80	28.75	0.440539	0.00942048	0.0543093
Table 2: Electrical resistivity (R), Viscosity (he), (a/f2)L for longitudinal wave and (a/f2)S for shear wave of GdAs at temperature (T) region from 2K to 80K.

Obviously from eqn. (3) h_e is inversely proportional to R-resistivity. As the intermetallic compounds GdP and GdAs have fewer carrier electron, the electrical resistivity values are quite high and h_e evaluated are small in general for all compounds. The ultrasonic attenuation both for longitudinal and Shear waves is directly proportional to h_e. Thus ultrasonic attenuation in these semimetallics is very low in comparison to pure metals as expected due to large resistivities of the substances. Due to smaller number of free carrier electrons available the ultrasonic attenuation arising from election-phonon interaction in GdP and GdAs is very small is general. The four curves for ultrasonic absorption coefficients over frequency square as a function of lower temperature (< room temperature) are qualitatively similar. At low temperature the ultrasonic absorption firstly decrease rapidly with increasing temperature and shows a kink at just above the Neel temperature T_N (fig 1-4). At higher temperature the absorption is linear with temperature. The Neel temperature as determined from the derivative ¶r/¶T are found to be 15.9, 18.7K for GdP and GdAs respectively. Although for GdP and GdAs electrical resistivity kniks in the curve of R vs. T, appear exactly at Neel temperature T_N 15.9 and 18.7K [11] but in plot of ultrasonic attenuation is T, kinks appear just above the Neel temperature approximately at 20K (fig 1-4) because here elastic behavior can be seen with SOEC values also affect the attenuation accordingly.

Fig 1: (a/f2) long. of Gdp vs. temperature

Fig 2: (a/f2) ) shear. of Gdp vs. temperature

Fig 3: (a/f2) long. of GdAs vs. temperature

Fig 4: (a/f2) shear. of GdAs vs. temperature

It can be understand with the tables 1-2 that shear wave attenuation (a/f²)_S in GdP and GdAs single Crystal is greater than the (a/f²)_L. Thus Although the attenuation in these compounds is smaller than pure metals, yet the trend of temperature dependence of (a) is of the same nature as for metal except some anomalous kinks due to anomalous physical parameters observed in Rare earth monopnictides.

References

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